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Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Joint Authors
Gao, Jianguo
Tan, Wei
Fan, Wenjun
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-31
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail.
By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived.
Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits.
Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point.
These results show the discrete model has more richer dynamics compared with the continuous model.
The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K)-βxy/N-(μ+m)x], y→y+δ[βxy/N-(μ+d)y].
Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
American Psychological Association (APA)
Tan, Wei& Gao, Jianguo& Fan, Wenjun. 2015. Bifurcation Analysis and Chaos Control in a Discrete Epidemic System. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060838
Modern Language Association (MLA)
Tan, Wei…[et al.]. Bifurcation Analysis and Chaos Control in a Discrete Epidemic System. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1060838
American Medical Association (AMA)
Tan, Wei& Gao, Jianguo& Fan, Wenjun. Bifurcation Analysis and Chaos Control in a Discrete Epidemic System. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060838
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060838